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LIBRARY 

OF THE 

UNIVERSITY OF CALIFORNIA. 

Class 



ISOMETRIC DRAWING 



Published by the 

McGraw-Hill Boole Company 

" 



to theBookDepartments of the 

McGraw Publishing Company Hill Publishing Company 

Publishers of Books for 

Electrical World The Engineering and Mining Journal 

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Metallurgical and Chemical Engineering 



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ISOMETRIC DRAWING 

A TREATISE ON MECHANICAL ILLUSTRATING 
DEALING WITH TYPICAL CONSTRUC- 
TIONS AND OUTLINING 



A COURSE IN THE ART 



BY 



ALPHA PIERCE JAMISON, M.E. 

Professor of Mechanical Drawing, Purdue University ; Junior Member of the 

American Society of Mechanical Engineers; Author of "Elements of 

Mechanical Drawing" " Advanced Mechanical Drawing," etc. 



MCGRAW-HILL BOOK COMPANY 

239 WEST 39TH STREET, XEW YORK 

6 BOUVERIE STREET, LONDON, E.C. 

1911 



Copyright, 1911 

BY 

McGRAW-HILL BOOK COMPANY 



PREFACE 

THE writer has been a teacher of mechanical drawing since 
the year 1895; during this time it has been his privilege and 
pleasure to instruct many students. 

As a part of the course administered, each student has been 
given some instruction and practice in Isometric Drawing; this 
practice has been limited, because of lack of time to devote to 
it (most of the time assigned being given to straight mechanical 
drawing), but has always been of interest to, and appreciated 
by, the student. 

Isometric Drawing is growing in popular usefulness, and one 
can hardly pick up a technical paper or magazine without 
finding one or more examples; its convenience and its adaptabil- 
ity are being recognized, and a knowledge of its execution is 
desirable and necessary for all draughtsmen. 

All treatments of the subject known to the writer accompany 
a treatise on Descriptive Geometry, or are too short; in every 
case the subject is treated with more attention to theory than 
to its practicability. 

The broad field for its use, its growing popularity, the enthu- 
siasm with which a student " takes hold," and the nature of the 
present (known to the writer) texts on the subject have led the 
writer to believe that a plain exposition of the " How " of the 
art, with no reference to the " Why," may be of some service 
to teachers, students, and draughtsmen. 

It is, therefore, with the object of presenting the subject 
in a new light or way, in the hope that others may find the art 
as useful as the writer has found it, in the hope of service, and 
not in the nature of a " This is better than thine " spirit, or in 
criticism of what has been written, that this work is offered. 

A. P. JAMISON. 

PUHDUE UNIVERSITY, WEST LAFAYETTE, IND., 
June 13, 1911. 

v 



227947 



CONTENTS 



CHAPTER I 

PRELIMINARY DISCUSSION AND EXPLANATIONS 

SECTION PAGE 

1. Introductory 1 

2. Definitions 1 

3. Uses of the Art 3 

4. Time element 8 

5. Characteristics 9 

6. Tools used 10 

7. Center lines and axes 11 

8. Flexibility 12 



CHAPTER II 
THE DRAWING OF PLANE FIGURES 

9. To draw a square 16 

10. To draw a hexagon 16 

11. To draw an octagon t 18 

12. To draw any polygon 19 

13. To draw a circle 20 

(a) First method 20 

(6) Second method 22 

(c) Error of the first method 22 

(d) To draw an inscribed hexagon 24 

(e) To draw a circumscribed hexagon 24 

(/) To draw a series of circles 25 

14. To draw an ellipse 26 

15. To draw an hyperbola 27 

16. To draw a parabola 27 

17. To draw an undulating figure 28 

1 8. To draw any figure composed of straight lines and circular arcs 28 

19. The proper arrangement of all drawings with reference to the center 

lines, and the manner of laying off dimensions 30 



viii CONTENTS 

CHAPTER III 

THE DRAWING OF SOLIDS 
SECTION PAGE 

20. Preparatory 32 

21. To draw a rectangular block 33 

22. To draw a pyramid of blocks 34 

23. To draw an hexagonal prism 35 

24. To draw an hexagonal pyramid 35 

25. To draw any rectangular solid which is of uniform or similar section . 36 

26. To draw any rectangular solid of variable section 38 

27. To draw a cylinder 39 

28. To draw a cone 40 

29. To draw a solid made up of circular arcs and straight lines 40 

30. To draw a ring, rectangular in section 41 

31. To draw a circular disc with holes in it 43 

32. To draw a stepped pulley 44 

33. To take out a section 45 

34. To draw an eccentric 46 

35. To draw an hexagonal nut 47 

36. To draw a hollow cylinder with a section removed 48 

37. To draw any solid of revolution 49 

38. To draw a ring, circular in section 51 

39. To draw screw threads 51 

40. To draw a sphere 54 



CHAPTER IV 
A COURSE IN ISOMETRIC DRAWING 

41. Explanatory 57 

42. Sheet No. 1, 

Isometric drawings of some plane figures 58 

43. Sheet No. 2, 

Isometric drawings of some straight-line objects 60 

44. Sheet No. 3, 

Isometric drawings of some bench exercises 62 

45. Sheet No. 4, 

Isometric drawings of some cylindrical objects 64 

46. Sheet No. 5, 

Isometric drawings of some shop tools 66 

47. Suggested sheets 68 

48. Remarks, 

Dimensioning 68 

Enlargement 68 

Distortion 68 

Shading 69 



ISOMETRIC DRAWING 



CHAPTER I 
PRELIMINARY DISCUSSION AND EXPLANATIONS 

1. Introductory. 

To understand what is to follow, the reader must possess a 
working knowledge of mechanical drawing; assuming this much, 
then, it is proposed to present the Art of Isometric Drawing 
with but very little preliminary or preparatory explanation. 
Attention is to be given to the way in which a drawing can be 
made, rather than to the reasons for doing " thus and so." 

Plain and common terms will be used in so far as they can be 
found to fit, and in the event a few unfamiliar words are used 
they must not be allowed to affect the reader's interest; as a 
matter of fact, the art is so simple, having but two principles 
or characteristics, that any draughtsman should have little, 
if any, difficulty in acquiring it. 

Students are urged, therefore, to read this work through 
carefully, to study;each successive step, as the subject is developed, 
to draw for themselves the several explanatory figures given 
in the text, and to further their working knowledge by the 
execution of the few plates given for this purpose in Chapter 
IV. Such attention will cover all of the essentials, and should 
furnish a knowledge of the art sufficient for practical use. 

2. Definitions. 

From an engineer's standpoint (so designated to distinguish 
it from the artist's standpoint), Drawing is divided into four 
main divisions, namely: Mechanical Drawing, Perspective Draw- 



2 " " 



DRAWING 




2 






\ 



PLATE No. 1. 



PRELIMINARY DISCUSSION AND EXPLANATIONS 3 

ing, Isometric Drawing, and Cavalier or Cabinet Projection 
or Drawing. 

Mechanical Drawing is the art of drawing each separate 
face of an object just as it is and not as it appears, and arrang- 
ing the several drawings so as to show the relation of the faces 
one to the other; Perspective Drawings are the same as pictures, 
and show the object as it appears from a definite viewpoint; 
Isometric Drawing is a kind of mechanical-perspective, or 
picture; and Cavalier Projection, a kind of mechanic al-isome trie- 
perspective drawing. 

Plate No. 1 illustrates the four kinds of drawings, Fig. 1 
being a two-view mechanical drawing, Fig. 2 (A and B) a 
perspective drawing, Fig. 3 an isometric drawing, and Fig. 4 
a cabinet drawing. The mechanical drawing requires two 
views to show the object (a part of a core box), while the per- 
spective drawing (Fig. 2 A), shows it in one view. 

In the mechanical drawing all parallel lines of the object 
are drawn parallel; in the perspective drawing three faces of 
the object are shown in one view; in the isometric drawing 
three faces of the object are shown in the one view, and all 
parallel lines of the object are shown parallel in the drawing; 
in the cabinet drawing one face of the figure is drawn as in the 
mechanical drawing, all parallel lines of the object are parallel 
in the drawing, as in isometric drawing, and the figure shows 
three faces in one view, the same as the perspective drawing. 

While it is true that one must have a knowledge of mechan- 
ical drawing in order to make an isometric drawing, the very 
opposite is true as to the reading of the two drawings, as one 
with no knowledge whatsoever of the principles of mechanical 
drawing is able to readily read an isometric drawing. A per- 
spective drawing is easily read by all, but it is hard to make 
unless one is more or less of an artist at free-hand work; an 
isometric drawing is easily made and readily read by all. 

3. Uses of the Art. 

Being familiar with the principles of mechanical drawing, 
the reader is also acquainted with the wide field for the use of 



ISOMETRIC DRAWING 




fe a 

o y 

o 



I f 

g 3 



PLATE No. 2. 



PRELIMINARY DISCUSSION AND EXPLANATIONS 5 

such drawings, for manufacturing and erecting purposes, in 
the shop and in the field, in books and catalogues, etc. Per- 
spective drawing is not much used in engineering drawing, its 
field being practically limited to architectural work. It is 
often desk-able to " picture " a machine or machine part or 
other object, and because of its adaptability it is here that 
isometric drawing finds its use. 

Plate No. 2 illustrates a three-view mechanical drawing of 
a bench-lathe leg, a perspective drawing of the leg, and an 
isometric drawing of the leg. A mechanical drawing is pri- 
marily a working drawing and lends itself to dimensioning; 
a perspective or isometric drawing is primarily an illustration 
or picture and is, in most cases, difficult to dimension. In fact, 
a perspective drawing can hardly be said to lend itself to dimen- 
sioning at all; an isometric drawing will permit dimensioning, 
though it is seldom done. 

Because of its similarity to perspective drawing and of the 
manner of execution, isometric drawing is sometimes called 
" Mechanical Perspective." Examples of its use are shown as 
follows: 

Fig. 1 1 is a copy of an illustration appearing in the Proceed- 
ings of the American Society of Mechanical Engineers (Vol. 29, 
page 172), and is one of four similar cuts illustrating a paper 
on the " Cost of Heating Store-houses." 

Fig. 2 2 is a copy of an illustration appearing hi a catalogue 
issued by a manufacturing company of their metal lumber, 
showing the framing of a house with then* product. 

Fig. 3 is an isometric drawing detailing the entrance to a 
building. 

Fig. 4 is a " bird's eye " view of an athletic field showing 
the enclosing wire fence, the bleachers and grandstand, the 
foot-ball and base-ball fields, and the running track. 

It is for such work as is illustrated by the just mentioned 

1 Reproduced by permission of the American Society of Mechanical Engi- 
neers and of Mr. H. O. Lacount, Boston, Mass., author of the paper mentioned. 

2 Reproduced by permission of the Berger Manufacturing Company, 
Canton, Ohio. 



ISOMETRIC DRAWING 




FIG. 1. 




FIG. 2. 



PRELIMINARY DISCUSSION AND EXPLANATIONS 7 

figures that isometric drawing finds its ready and best use, 
that is, in drawings where most of the lines are straight lines 




FIG. 3. 



and the objects drawn are of a rectangular character. It is 
possible, however, to draw many kinds of irregular objects, 
as is evidenced by the illustrations of the text. 



8 



ISOMETRIC DRAWING 



4. Time Element. 

While isometric drawing is limited to certain uses because 
of the nature of the object and the purpose of the drawing, 
the real, practical limitation to the art is the time required to 
execute the drawings. 

The author has on several occasions made comparison of 
the time required in which to draw a mechanical drawing and 
the time consumed in making an isometric drawing; he has 
timed himself, and has taken the time of a number of students, 
and finds that, with the exception of very simple rectangular 
objects, it requires more time to make an isometric drawing 




FIG. 4. 

than it does to execute a mechanical drawing the increase in 
time required depending entirely upon the nature of the object. 
For some very simple objects it was found that an isometric 
drawing could be made in a little less time than that required 
for making a mechanical drawing; for a large number of simple 
rectangular objects, with few curves and circular holes or 
cylindrical parts, it was found that the time required for the 
two kinds of drawings about balanced; as the object drawn 
became more complex, having cylindrical and curved members, 
nuts, threads, etc., to draw, the time required varied from 
30 to 200 per cent more time for isometric drawings than for 
straight mechanical drawings, the average being about 80 per 
cent. 



PRELIMINARY DISCUSSION* AND EXPLANATIONS 



9 



In general, therefore, it may be said that isometric drawing 
requires from 50 to 100 per cent more time for its execution 
than mechanical drawing. Of course, some objects will require 
several hundred per cent more time; but it is surprising, in 
the field for which it is best adapted and for the purpose for 
which the drawing is most used, how many illustrations may be 
made with isometric drawings with but very little increase in 
time taken over that required for making a mechanical drawing. 

5. Characteristics. 

It has been stated (Article 1) that isometric drawing has 
but two principles. Such a statement is speaking broadly, and 




FIG. 5. 



should be further qualified by adding, " which are new to one 
already familiar with the principles of mechanical drawing." 

Isometric drawing is based on isometric projection, and 
isometric projection is the result of a particular kind of pro- 
jection and has a certain definite underlying principle. This 
work being an exposition of the " How " of the art, the develop- 
ment and the further explanation of the theory are purposely 
omitted. 

In mechanical drawing the center lines, dimensions, and 
reference lines are drawn horizontally and vertically, and a 
view is given for illustrating each face of the object drawn; 
in isometric drawing the center lines, tlimensio.ns-aftd-retefence 
lines are drawn at an angle with the horizontal and vertical, 



10 



ISOMETRIC DRAWING 



and three faces are shown in one view or drawing. The two 
characteristics of isometric drawing, as compared with ordinary 
mechanical drawing, are, therefore, the direction of the principal 
lines and the showing of the three dimensions of an object in 
one view. (See Fig. 5.) 

6. Tools Used. 

The tools required for making isometric drawings are prac- 
tically the same as those needed for ordinary mechanical 




FIG. 6. 




FIG. 



drawing (Fig. 6), the only difference being in the triangles. 
The principal lines in isometric drawing are either horizontal, 
vertical, or 30 or 60 to the horizontal, and are drawn with 
the 30-60 triangle and T-square, the 45 triangle so much used 
in mechanical drawing being dispensed with (Fig. 7). 



PRELIMINARY DISCUSSION AND EXPLANATIONS 11 

All of the figures given in the text oan be drawn in pencil 
with the following tools: A drawing board; a T-square; a 
30-60 triangle; a pencil compass; an irregular curve; and the 
necessary paper, pencil, and scale or ruler. To ink the drawings 
requires the usual pens and ink. 

7. Center Lines and Axes. 

An object has three dimensions, namely, length, width or 
breadth, and height or thickness. In mechanical drawing two 
of these dimensions show in any one view, but it requires 
a second view to give the third dimension. In isometric draw- 
ing three dimensions are given in one view. 

In laying out a mechanical drawing it is the usual practice 
to work to some reference line. This line is usually a center line, 
and is either horizontal or vertical. When two center lines are 
used, they are drawn at right angles one to the other. This 
method is also used in isometric drawing. 

Fig. 8 is an isometric drawing of three planes, a-b-c-d and 
e-f-gh being vertical planes and i-j-k-L a horizontal plane. A 
pah- of center lines are show^n drawn on each plane, the lines 
5-5 and 6-6 being on the horizontal plane and the lines 3-3, 
4-4, 1-1, and 2-2 being on the vertical planes. They are show r n 
in the conventional manner at A, B, and C, respectively. All 
of these center lines, regardless of the plane in which they lie, 
would be shown in mechanical drawing, as illustrated at D. 

The three planes shown are those most usually assumed 
in drawing, and it is important that the reader note the char- 
acteristics of the three sets of lines, as these lines determine 
the plane of the drawing. The lines shown at A are at 30 
with the horizontal, are drawn with the T-square and 30 triangle 
(the 30 angle of the 30-60 triangle), and are characteristic 
center lines for use when drawing on a horizontal plane. The 
lines shown at B are drawn, one vertical and one at 30 with 
the horizontal (with the T-square and 30 triangle), and are 
characteristic center lines for use when drawing on what may 
be termed a left-hand vertical plane. The center lines shown 
at C are drawn, one vertical and one at an angle of 30 with the 



12 



ISOMETRIC DRAWING 



horizontal, and are characteristic center lines for use when 
drawing on what may be termed a right-hand vertical plane. 
When drawing in any one of the above three planes the draw- 
ing is limited to two dimensions only plane figures; to repre- 
sent objects with three dimensions solids a third principal 
line of reference is used, called an axis. The dashed lines 
shown at A, B, and C of Fig. 8 represent such lines, and, as 




I 



FIG. 8. 



in the cases A, B, and C mentioned above in connection with 
characteristic center lines, are characteristic axes for isometric 
drawings. 

8. Flexibility. 

The center lines and axes just described are the basis or base 
lines for all isometric drawing, and as long as the relation 
between the three lines as shown in Fig. 8 is maintained they 
may be drawn at will. For practical purposes the direction 
of the lines is determined by -the drawing tools used, the T-square 
and triangle. The four usual arrangements are shown at a, 
b, c, and d of Fig. 9. 

Being thus able to select a number of directions for drawing 



PRELIMINARY DISCUSSION A^D EXPLANATIONS 13 



the axis of a drawing, isometric drawing permits an object to 
be shown in a number of different positions, as illustrated at 








FIG. 9. 

A, B, C, and D, Fig. 9, and at 5-1, B-2, 5-3, 5-4, 5-5, Fig. 
39. 




FIG. 10. 



In addition to being able to show an object in different 
positions, sections may be shown in isometric drawings the same 
as in ordinary mechanical drawing. 



14 



ISOMETRIC DRAWING 




PLATE No. 3. 



PRELIMINARY DISCUSSION AND EXPLANATIONS 15 

Plate 3 illustrates the flexibility of the art: Fig. 1 is a two- 
view mechanical drawing of a loose pulley, the face view show- 
ing a half section; Fig. 2 is an isometric drawing of the pulley, 
showing the same section removed as in Fig. 1 ; and Figs. 2, 3, 
and 4 show the pulley in different positions. 

Fig. 10 is a three-view mechanical drawing of an indicator 
cock or valve, and an isometric drawing of the same valve. 
The drawings show a section of the valve removed to show 
the interior. 

Plate 3 and Fig. 10, together with the other illustrations 
of the text, serve to demonstrate the flexibility of the art. 



f 




CHAPTER II 
THE DRAWING OF PLANE FIGURES 

9. To Draw a Square. 

Fig. 11 illustrates a square drawn in different positions, 
drawing A being a mechanical drawing and drawings B, C, and 
D isometric drawings. Drawing B represents the square as 
lying on the horizontal plane; and drawings C and D as lying 
on vertical planes. 

To construct the square (consider drawing ), draw the 
center lines 5-5 and 6-6 with the T-square and 30 triangle, 

each line being at 30 with 
the horizontal. Next, as- 
suming the square to be V 
on a side and working from 
the intersection of the center 
lines, o, lay off, each way 
from the point o, on each 
center line, a distance of \ n ', 
or one-half of the length of 
a side of the square, and lo- 
cate the points 6, 6 and 5, 5. 

Lastly, draw through each of the two points on each center line 
a line parallel to the other center line; these lines will meet 
and will form the required figure, a-b-c-d, as shown. 

Drawings C and D are drawn in like manner, the only dif- 
ference being in the direction of the center lines, which may, 
however, be drawn, as before, with the T-square and 30-60 
triangle. 

10. To Draw a Hexagon. 

Fig. 12 represents the drawing of a hexagon, drawing A 
being a mechanical drawing, and drawings B-I, B-2, C, and D 

16 




FIG. 11. 



THE DRAWING OF PLANE FIGURES 



17 



isometric drawings. Of the isometric drawings, B-l and B-2 
are on horizontal planes and drawings C and D on vertical 
planes. 

In mechanical drawing the drawings are always drawn 
square with the center lines, as shown at A, and not as shown 
at E- } this custom prevails because of the better appearing 
drawings produced and because of the greater convenience and 
speed secured when executing the drawing. This method of 
drawing things square with the center lines is followed in iso- 
metric drawing. 

To construct the hexagon (consider drawing 5-2), first 
draw the center lines 5-5 and 6-6 at the angle shown. Now 




FIG. 12. 

a hexagon has two so-called diameters or dimensions, namely, 
the distance between opposite sides or flats, as distance 7-7, 
drawing A, and the distance between opposite corners, the 
diagonal distance, as distance a-d, drawing A. Second, work- 
ing each way from the intersection of the two center lines, o, 
lay off one-half of the diagonal distance on one center line, 
and one-half of the flat distance or dimension on the other 
center line. This gives the points a, d y 5, and 5, respectively, 
Third, draw lines through the points obtained by laying off 
the flat diameter of the hexagon, the points 5 and 5, and on 
each line lay off, each way from the point through which the 
line is drawn, one-half of the length of a side of the hexagon. 
This gives the points 6, c, e, and /. Fourth, and lastly, connect 



18 



ISOMETRIC DRAWING 



the six points now located, as shown, giving the required figure. 
[See also Article 13, (d) and (e).] 

11. To Draw an Octagon. 

Fig. 13 shows an octagon a mechanical drawing of the 
figure at A, an isometric drawing on a horizontal plane at B, 
and isometric drawings on vertical planes at C and D. 

The figure may be constructed in two ways : 
First method (consider drawing C). 

Draw the center lines 1-1 and 2-2. On these center lines 
construct the " square of the octagon," b-d-f-h, as shown, 

and as explained in Article 
9. Next, working from the 
intersection of the center 
lines, o, lay off each way 
on each center line, one- 
half of the diagonal distance 
or diameter of the octagon. 
This gives the points a, c, 
e, and g. Lastly, join the 
eight points, as show r n, and 
form the octagon. 
Second method (consider drawing D). 

This method is by referring all of the points to the center 
lines. In drawing A, consider points a, 6, c, d, e, /, g, and h 
projected (perpendicularly) onto the center lines, giving on 
center line c-g the points c, x, o, y, and g, and on line a-e the 
points a, m, o, n, and e. To draw the isometric drawing D, 
first draw the center lines as shown, and, working from point 
o, lay off on each the corresponding above-mentioned projected 
points ; that is, on line a-e, lay off points a, m, o, n, and e, and 
on line c-g points c, x, o, y and g. Second, through the points 
x and y on line c-g draw indefinite lines (such as lines b-x-d 
and h-y-f) parallel to center line a-e. Third, draw indefinite 
lines through the points m and n on center line a-e parallel 
to center line c-g. These two lines will intersect the pair first 
drawn and will locate points b, d, f, and h. The points a, c, e, 




FIG. 13. 




THE DRAWING OF PLAXE FIGURES 19 

and g, being on the center lines, are fixed, and, to finish the 
figure, connect the eight points found, as shown. 

When an octagon on a horizontal plane lies within a cir- 
cumscribing circle, the construction of the figure is much 
simplified thereby. In such a 
case, Fig. 14, first draw the 
center lines 5-5 and 6-6. Sec- 
ond, draw the circumscribing 
circle (the construction of a 
circle is given in Article 13). 
Third, draw a horizontal and 
a vertical line through the 

intersection of the center lines, 

point o. Fourth, and lastly, join the eight points in which the 
center lines and the last drawn two lines cut the circumference 
of the circle. 1 It is obvious that a similar construction can 
be applied when drawing on a vertical plane 

12. To Draw Any Polygon. 

Fig. 15 represents the construction of a ten-sided figure and 
of a fifteen-sided figure, and is typical of any polygon. The 
method shown is what may be called " plotting," and is based 
on the reference of all points to the center lines. In any plane 
figure each and every point has two dimensions, so to speak. 
For example, a point is so far from each of the two center lines; 
in drawing A-l, point c is c-5 (or 4-0) distance from the vertical 
center line, and c-4 (or 5-o) distance from the horizontal center 
line. Xow if these distances are known, they may be laid off 
on the center lines, a line drawn through the point on one center 
line parallel to the other center line, and the point located by 
the intersection of the lines drawn. 

To construct the fifteen-sided figure : 

In drawing A-2, project all of the points onto the vertical 
center line (giving points a, 15, 16, 17, o, 18, 19, 20, and 21), 
then all onto the horizontal center line (giving points 1, 2, 3, 4, 
5, 6, 7, o, 8, 9, 10, 11, 12, 13, and 14). Second, draw the iso- 

1 The isometric drawing of a circle is an ellipse, but is spoken of as a 
" circle." 



20 



ISOMETRIC DRAWING 



metric center lines a-21 and 1-14 (drawing B-2), and, working 
from their point of intersection, o, lay off the points a, 15, 16, 
17, o, 18, 19, 20, and 21 on the line a-21 and the points 1, 2, 3, 
4, 5, 6, 7, o, 8, 9, 10, 11, 12, 13, and 14 on the line 1-14. Third, 
draw lines through the points on line a-21 parallel to line 1-14, 
then lines through the points on line 1-14 parallel to line a-21. 
The intersection of the two lines drawn through the point on each 
of the two center lines obtained (at the start) by the projection 
of any corner onto the center lines, locates the point in question, 
and the series of lines the several points a, 6, c, d, etc. Lastly, 
join the points as shown. 





a-l 



FIG. 15. 



In cases where the necessary dimensions for executing the 
drawing cannot, readijy be obtained from the object, it is neces- 
sary to first construct a mechanical drawing of the part or detail 
in question, to draw the center lines of the figure, and to pro- 
ject the point or points on these lines (as in drawings A-l and 
A-2)', then take up the isometric drawing, using the distances 
or dimensions thus obtained for its construction. 

13. To Draw a Circle. 

Figs. 16 'and 17 are drawings of a circle, and represent two 
methods of construction. 
(a) First method. ^ 

Fig. 16, illustrates the mechanical drawing of a circle (draw- 



THE DRAWING OF PLANE FIGURES 



21 



ing A) and the isometric drawing of a circle (drawings B, C and 
D), drawing B being on a horizontal plane and drawings C 
and D on vertical planes. 

To construct the figure (consider drawing B), first draw the 
center lines a-b and c-d, each at 30 with the horizontal. Second, 
working from the intersection of the two center lines, o, lay off 
on each center line, each way from point o, a distance equal 
to the radius of the circle. This gives points a, 6, c, and d. 
Third, through each of the two points on each center line draw 
a line parallel to the other center line. These four lines will 
form a diamond-shaped figure (a parallelogram), 1-2-3-4. 




FIG. 16. 

Fourth, with the point 2 as a center and the distance from the 
point to the middle of the opposite side of the parallelogram, 
distance 2-c, as a radius, describe the arc'c-6. Fifth, with the 
point 4 as a center and a radius equal to the distance from the 
point to the middle of the opposite side of the parallelogram 
as a radius, distance 4-J, describe the arc a-d. Sixth, draw 
the diagonal of the parallelogram, the line 1-3, and where 
this line intersects the lines 2-c and 4-d, the points x and y, 
take new centers and, with a radius equal to the distance from 
either point to the middle of the nearest sides of the parallelogram 
such as distances x-c or y-d, draw the arcs a-c and b-d, com- 
pleting the ellipse a-d-b-c the isometric representation of the 
circle. 



22 



ISOMETRIC DRAWING 



The ellipse or " circle " in drawing C or D, the plane of 
which is vertical, is drawn in a manner similar to that just 
described. The method just explained is an approximate 
method. 
(6) Second method. 

Fig. 17 illustrates a second method of constructing an iso- 
metric drawing of a circle. In the figure, drawing A is a mechan- 
ical drawing and drawing B an isometric drawing. The method 
shown is similar to that employed in Fig. 15 and described in 
Article 12, and is what has been termed plotting. 

To construct the figure, first draw the mechanical drawing 
of the circle (A), divide the circumference into any number 





FIG. 17. 

of points, project these points onto the center lines, then take 
up the isometric drawing. In this (drawing B), the center 
lines are drawn; the points of division, V, a, 6, c, o } etc., obtained 
by the projection of the points of division of the circle onto the 
center lines (drawing A), laid off; lines drawn through the 
points of division as show r n; the points 4, 5, 6, etc., located by 
the intersection of the lines; and the closed curve V, 4, 5, 6, 
etc., obtained by drawing a smooth curve through the points 
found all as suggested and shown by the figure. 

The method just described is an exact method. 
(c) Error cf the first method. 

The two methods given for making an isometric drawing 
of a circle are shown applied in Fig. 18, the circle (so called) 
a-b-c-d being drawn by the first, or approximate, method, and 



THE DRAWING OF PLANE FIGURES 



23 



the circle a-e-b-f-c-g-d-h drawn by the second, or exact, 
method. 

An inspection of the figure shows that the approximate 
method gives a representation which is shorter and wider than 




FIG. 18. 

that obtained by the exact method. The approximate method, 
being the easier of application, is the one used practically, and 
because of its two errors sometimes leads to slight comph* ca- 
tions in the construction of drawings; for example, when the 
circle joins or fits into or about some other figure or part, as 
when drawing a sphere, a circumscribing or inscribed circle, etc. 

Fig. 19 illustrates a circle drawn by the two methods already 
given, the dotted curve being drawn by the approximate method 
and the full-line curve by the 
exact method; also, the draw- 
ing of a hexagon, in two posi- 
tions, about the true circle 
(Article 10). The particular 
points to be noted in this 
figure are that in either hexa- 
gon the length of each of the 
two sides which are parallel 

with one of the center lines (a-b and d-e or h-4 and k-T) is the 
true length of a side of the hexagon, and that each of these 
two lines (a-b and d-e, or h-i and k-l) is symmetrical with the 
center line (being divided into two, a-b and d-e at H, and h-i 
and k-l at V). 

Fig. 20 illustrates a circle drawn by the approximate method, 
and an inscribed (the dashed-line figure) and a circumscribed 




FIG. 19. 



24 ISOMETRIC DRAWING 

(the full-line figure) hexagon. The dotted hexagon A'-B'-C-D' 
-E f -F is a correct drawing of the circumscribed hexagon 
without reference to the circle and shows, at the corners A', B', 
D', and E' } the error of a hexagon drawn with reference to a 
circle drawn by the approximate method. 

The particular feature to note in this figure is that in the 
hexagon the two sides (A-B and D-E or a-b and d-e, which are 
drawn parallel with the center line 7-7, are unsymme trie al with 
the center line H-H, being longer on one side (H-B and H-E 
or h-b and h-e) than on the other (A-H and H-D or a-h and 
h-d). 

The convenience of the approximate method for drawing 
a circle, and the large number 
of circles and circular arcs 
always to be drawn more 
than outweigh the errors 
(such as described above) in- 
troduced by its adoption and 
application. In cases where 
a discrepancy shows up, it p IG 20. 

will be but slight, and it is 

customary and an easy matter to adapt the lines so as to make 
the conditions fit. 

(d) To draw an inscribed hexagon. 

To draw a hexagon within a circle (Fig. 20), first draw 
the circle by the approximate method [Article 13 (a)]. Where 
the center line VV cuts the circle, points c and /, locates 
two points , of the hexagon. Second, working from, point o, 
lay off on the center line H-H, each way from o, one-half of 
the distance between sides of the hexagon, the length o-h, and 
draw through each of the two points thus obtained a line parallel 
to the center line 7-7. Where these lines cut the circle, points 
a, b, d, and e, locates four points of the hexagon. Third, join 
the six points found, and the hexagon a-b-c-d-e-f is obtained. 

(e) To draw a circumscribed hexagon. 

To draw a circumscribed hexagon (Fig. 20), first draw the 
isometric representation of the circle by the approximate 




THE DRAWING OF PLANE FIGURES 



25 



method. Second, working from the point o, lay off on the center 
line V-V, each way from o, one-half of the distance between 
corners of the hexagon (the lengths o-C and o-F). This locates 
two points (C and F) of the hexagon. Third, through each 
of the points H, in which the center line H-H intersects the ellipse 
H-X-Y-H, etc ., draw a line parallel to center line V-V. Fourth, 
from the points C and F draw lines, each way, tangent to the 
circle (points X, Y } M, and N) intersecting the lines drawn 
through the points H parallel to line V-V. The intersection 
of these lines locates the remaining four corners of the hexagon, 
and the construction completes the drawing of the figure. 
(/) To draw a series of uniform circles the centers of which lie in 
the same straight line and plane. 

Fig. 21 illustrates a number of uniform circles with centers 
in a common straight line, drawing A being a mechanical 
drawing and drawing B an isometric drawing. 




FIG. 21. 

To construct the isometric drawing, first consider one circle 
only, as, for example, the circle r-l-s-1 of drawing A f and draw 
the isometric representation of this circle by the approximate 
method [Article 13 (a)], as shown in drawing B by the parallelo- 
gram a-b-c-d } the radii /, g, h, and i, and the ellipse r-l-s-1. 
Second, extend the center line r-s, the lines a-b and d-c } and 
through the points x and Y draw lines parallel to the above 
lines, all as shown by the line s-s 2 and the dashed lines b-m, 
c-p, x-n and Y-O, respectively. Third, lay off on the line d-p 
the distances d-di, and d^d 2 equal to the length e, the distance 
between centers of the circles; and, with a radius equal to 
radius h and the points d lt d 2 as centers, describe the arcs 2-Sj 



26 



ISOMETRIC DRAWING 



and 3-s 2 (parallel to the arc 1-s). Fourth, locate the points 
bi and b 2 in like manner and, with these points as centers and 
a radius equal to radius g, draw the arcs r x -2 and r 2 -3 (parallel 
to the arc r-1). Fifth, lay off on the line x-n the distances 
x-x x and Xj-x-j equal to the length e, the distance between cen- 
ters of the circles and, with the points x x and x 2 as centers and 
a radius equal to radius/, draw the arcs 2-r, and 3-r 2 . Sixth, 
and lastly, locate the points YJ and Y 2 in a similar manner and, 
with these as centers and a radius equal to the radius i, draw 
the arcs 2-s 1; and 3-s 2 , completing the figure. 

A considerable amount of labor of construction is eliminated 
by keeping the above scheme in mind, and it is offered to call 
attention to the fact that there are many such " short cuts " 
which will become apparent after some little practice in the art, 
and which should always be taken advantage of. 

14. To Draw an Ellipse. 

Fig. 22 illustrates the drawing of an ellipse. A is the mechan- 
ical drawing, and B the isometric drawing. The isometric 
drawing is shown on a vertical plane. 




FIG. 22. 

To draw the figure, first divide the ellipse as drawn at A 
into a number of points, as points a, &, c, etc.; then project 
the points onto the center lines as shown by the points 1, 2, 3, 
4, etc. Second, draw the center lines H-H and V-V of draw- 
ing B, and on them lay off the corresponding divisions on the 
center lines of drawing A, points 1, 2, 3, 4, etc. Third, through 
the divisions on each center line draw lines parallel to the other 



THE DRAWING, OF PLANE FIGURES 



27 



center line. The point in which the lines through the two points 
on the center lines (one on each) representing the projection 
of any one point intersect, will locate that particular point, 
and the series of lines the several points a, b, c, etc. Fourth, 
and lastly, through the points thus obtained and the points 
H, H and V, V, the ends of the axes of the ellipse, draw the 
curve H, a, b, c, etc., the isometric drawing of the ellipse. 

15. To Draw an Hyperbola. 

Fig. 23 illustrates an hyperbola. Drawing A is the mechan- 
ical, and drawing B the isometric drawing. The feature of 
this figure is that it has but one center line (line 1-e) and intro- 
duces the use of a second line of reference which may be called 
a base line (line 5-12). 





FIG. 23. FIG. 24. 

To draw the figure, first divide the curve into a number of 
points, as points a, b, c, etc., of drawing A; then project each 
point into the center line and onto the base line, thus obtaining 
the points 1, 2, 3, etc. Second, draw the center line 1-e and the 
base line 5-12 of drawing B, and on them lay off the points 
1, 2, 3, etc. Third, draw lines through each of these points 
as shown and locate the points a, 6, c, etc. Fourth, through 
the points thus located draw the curve a, b, c, etc., the isometric 
drawing of the hyperbola. 

16. To Draw a Parabola. 

Fig. 24 illustrates two drawings of a parabola, drawing A 
being a mechanical drawing and drawing B an isometric drawing. 



28 ISOMETRIC DRAWING 

The construction is the same as described in Article 15, 
and is clearly shown by the figure. 

17. To Draw an Undulating Figure. 

It will have been noted that most of the figures given thus 
far are shown drawn on the horizontal plane, Figs. 17, 18, 19, 20, 
and 21, for example, and that the last three, Figs. 22, 23 and 24, 
are drawn on vertical planes. This is done to acquaint the 
reader with the flexibility of the art (Article 8), and to illustrate 
the procedure on the two planes. To further illustrate the 
choice of position or plane in which to draw, Fig. 25 is offered. 
It illustrates the drawing of an undulating figure made up 




of semicircles, and shows the drawing on what may be termed 
an oblique plane the center lines for which agree with those 
illustrated in Fig. 9 at d. 

To draw the figure, draw the horizontal line H-H and on 
it lay off the points a, b, c, and d, a distance apart equal to the 
distance between centers of the circular arcs as shown in drawing 
A. Second, through each point draw a center line V-V at 60 
with the horizontal. Third, on each pair of center lines, such 
as H-H and V-a-V, lay out the necessary lining and construct a 
semicircle as described in Article 13 (a), and, as shown by the 
figure, the series of semicircles will form the required figure. 

18. To Draw Any Figure Composed of Straight Lines and Cir- 
cular Arcs. 

Fig. 26 illustrates the drawing of a figure made up by a 
combination of straight lines and circular arcs. The iso- 



THE DRAWING OF PLANE FIGURES 



29 



metric drawing B is on a vertical plane, and the construction 
very similar to that described in Article 17. 

To construct the figure, first draw the center line H-H at 
30 with the horizontal, and on it lay off the center points 
a, 6, c, and d, corresponding to the center points a, b, c, and d 
of drawing A. Second, through each point draw a center line 
V-V, and on each pair of center lines thus formed proceed with 
the lay-out for drawing a circle by the approximate method 
(Article 13), and obtain the centers and radii necessary to 
describe the arcs of the figure all as illustrated. Lastly, 
connect the circular arcs with straight lines as shown. 

Combinations of straight lines and circular arcs are very 
frequent in drawing and it is important that the draughtsman 




FIG. 26. 

know how to treat them. Sometimes they are in such a form 
that a beginner does not recognize or think of them as such. 
One of the examples most frequently met, with is the represent- 
ing of round corners of figures and objects. 

Fig. 27 illustrates a square with rounded corners. It will 
be noted from an inspection of the figure that the arcs at the 
corners are circular arcs, and that they may be continued 
to form complete circles and the figures to come under a con- 
struction as given for Fig. 26. 

To construct the isometric drawing B, first draw the center 
lines H-H and V-V, and construct the square W-X-Y-Z 
(Article 9). Second, consider the lower left-hand corner of 
the figure, W, and from the corner lay off, each way, a distance 
equal to radius R, as lengths W-f and W-e' } through the points 



30 



ISOMETRIC DRAWING 



thus obtained, points / and e, draw the center lines /-/ and e-e. 
Third, working to the center lines just found, use the approx- 
imate method for drawing a circle (Article 13), and locate the 
center point o and the radius r, and describe the full-line arc 
f-e, that portion of the ellipse f-e-f-e forming the rounded 
corner in question. Fourth, in a similar manner draw in the 
full-line curve a-b at corner X, as shown by the drawing. 

The curves at corners Y and Z may be obtained in a similar 
manner, though with a little less work. That is, now that the 
scheme is known, in applying the method for drawing a circle, 
only that portion of the entire construction used for the drawing 




FIG. 27. 

of a circle needed to locate the center point and the necessary 
radius need be drawn, the construction being clearly shown in 
the figure. 

19. The Proper Arrangement of All Drawings with Reference to 
the Center Lines, and the Manner of Laying Off Dimen- 
sions. 

It will have been noticed that all of the constructions given 
thus far begin with the drawing of the two center lines, and that 
the figures then drawn are drawn square with the center lines. 
Also, that the dimensions are all laid off on the center lines, 
or on lines parallel to the center lines. This is the correct 
practice in isometric drawing, and is but in strict accordance 
with the usual and accepted practice in ordinary mechanical 
drawing. 



THE DRAWING, OF PLANE FIGURES 



31 



Fig. 28 shows at drawings A and ^.-1 the usual placing of 
a hexagon with reference to the center lines; drawing A-2 
shows an unusual arrangement. When such an arrangement 
is to be drawn in isometric, the corners of the hexagon must 
be referred to the center lines and the points located by plotting, 
as directed in Article 12, and as shown by drawing B-2. 

It may be well to note the four right angles formed by the 
center lines in drawings A-2 and B-2. The angle 7-0-1 of 
drawing A-2 is shown as 7-0-1 
of drawing B-2 (note that 
this angle as drawn is more 
than a right angle, but in 
isometric drawing is used as 
and called a right angle), 
and the angle 7-0-6 of draw- 
ing A-2 is shown at B-2 as 
the angle 7-0-6 (note that 
this angle as drawn is less 
than 90, but is used as and 
called a right angle). The 
other two angles are readily 
noted in the figure. 

In mechanical drawings the two dimensions of plane figures 
are always either vertical or horizontal; in isometric drawing 
one dimension is sometimes vertical and sometimes horizontal 
(never one horizontal and the other vertical), and when it is 
so the other dimension is always at an angle to the horizontal 
or vertical (see Article 8), the arrangement depending upon 
the arrangement of the center lines of the figure in question. 

It should be remembered, therefore, to always lay off dimen- 
sions parallel with the center lines of the figure drawn, and when 
measuring an isometric drawing to scale it in directions parallel 
with the center lines. 




A-2 



FIG. 28. 



CHAPTER III 
THE DRAWING OF SOLIDS 

20. Preparatory. 

The student is cautioned not to attempt the reading of this 
chapter without first reading Chapter II and mastering, in so 
far as possible, the principles and methods there set forth. 
The drawing of solids is based on the drawing of plane figures, 
and the only new feature introduced in this chapter is the 
drawing on different planes, not as set forth in Article 8 and as 
illustrated by the figures of Chapter II, exactly, but the drawing 
on all of the planes mentioned, possibly in the same illustration, 
with a definite relation as to position to all of the other planes. 

If one has a thorough knowledge of the methods given in 
Chapter II, the only difficulty likely to be encountered when 
making isometric drawings of solids is to get the drawing of any 
particular feature of the object drawn on the correct plane. This 
is the one difficulty which is of serious moment to the beginner, 
and requires some little experience and practice to eliminate. 
To reduce such trouble to a minimum the student should care- 
fully consider the part in question, note the plane (horizontal 
or vertical) on which it lies, then note the center lines of the 
plane of his drawing. If the center lines are drawn as set forth 
in Article 7, the correct plane can always be established. 

A second, minor, difficulty often encountered is to get the 
correct position of the plane on which to draw. This is a matter 
of dimension and lay-out, and the difficulty can only be eliminated 
by the student's keeping in mind that all dimensions must be 
laid out along lines which are parallel w r ith the center lines 
or axis of the figure or drawing. 

Coming now to the drawing of solids, the drawings have 
three dimensions, and use is made of the third of the three lines 

32 



THE DRAWING OF SOLIDS 



33 



mentioned in Article 7 (the axis) and illustrated in Fig. 8 at 
.4., Bj and C, and Fig. 9 at a, 6, c, and d. These three lines are 
the basis of all of the constructions which follow. 

21. To Draw a Rectangular Block. 

Fig. 29 is an illustration of a rectangular block, drawing A 
being a mechanical drawing and drawings B, B-l, and B-2 
isometric drawings. The isometric drawings show the block 
in three different positions, also three different constructions. 
All of the constructions are simple, but should be considered. 
They are : 



-h- 

i - 









1. To construct drawing B, first draw the center lines 
H-H and V-V, and on them construct the rectangle 1-2-3-4 
as explained in Article 9, the size of the rectangle to agree with 
the dimensions of the top face of the block. Second, draw^ 
the line X-Y (the axis for the center lines H-H and V-V, 
Article 7) and on it lay off a length o-o' equal to the thickness 
of the block. Third, through the point o' draw the center lines 
h-h and v-v, and working to these construct the rectangle 
5-6-7-8. Fourth, and lastly, join the points 1 and 5, 2 and 6, 
etc., completing the figure as shown. 

2. To construct drawing Bl, first draw the center lines H-H 
and V-V and on them construct the face 1-2-3-4. Second, 
draw the axis for the center lines just used, line XY, and on 
it lay off the length of the block and locate the point o l '. Third, 
through the point o' draw center lines, and working to them 



34 



ISOMETRIC DRAWING 



construct the face 5-6-7-8. Fourth, join the corners of two 
bases as shown. 

3. To construct drawing B-2, first draw the face 1-2-3-4 
as in the second construction. Second, through the points 
1, 4, and 3, draw lines parallel to the axis of the block, and on 
them lay off lengths equal to the length of the block. This 
locates points 5, 8, and 7. Third, join the points 5 and 8, and 
7 and 8. 

22. To Draw a Pyramid of Blocks. 

Fig. 30 illustrates a number of square blocks, piled one upon 
the other in such a manner as to keep the pile symmetrical. 




FIG. 30. 

To construct the isometric drawing (B), first draw the center 
lines a-a and b-b, and on them construct the square 1-2-3-4, 
as explained in Article 9. Second, from the corners 1, 3, and 4, 
drop vertical lines, and on the line through the point 4 lay off 
a length 4-4' equal to the thickness of the block. Third, through 
the point thus located (point 4') draw the lines 4 '-3' and 4'-l' 
parallel to the center lines a-a and b-b, respectively. Fourth, 
through the intersection of the center lines, point o, draw the 
axis X-Y, and on it lay off a length equal to the thickness of 
the top or smallest block. Fifth, through the point thus located, 
point o', draw the center lines c-c and d-d', working to them 
construct the square 5-G-7-8 and finish the drawing of the out- 



THE DRAWING OF SOLIDS 



35 




line of the second block, all in a manner similar to the drawing 

of the first block. Sixth, establish the plane of the top of the 

third block by dropping down 

from point o' to o" a distance 

equal to the thickness of the 

second block and drawing the 

center lines e-e and f-f, and 

construct the outline of the 

third block as shown. Seventh, 

proceed in a similar manner 

for the construction of the 

fourth block, and complete the 

figure. 

23. To Draw an Hexagonal Prism. 

Fig. 31 illustrates the con- FIG. 31. 

struction of an hexagonal prism. 

To construct the figure, first draw the center lines a-a and b-b, 
and on these construct the hexagon 1-2-3-4-5-6, as explained 
in Article 10. Second, draw the axis of the figure, the line 
X-Y, and on it lay off a length o-o' equal to the length of the 

prism. Third, through the 
point o' draw the center lines 
c-c and d-d, and working to 
them construct the hexagon 
l'_ 2 '-3'-4'-5'-6'. Fourth, 
join the comers of the two 
bases as shown, completing 
the figure. 

24. To Draw an Hexagonal 
Pyramid. 

Fig. 32 illustrates the con- 
struction of an hexagonal 
pyramid. 

To construct the figure, first draw the center lines a-a and 
6-6, and working to them construct the hexagon 1-2-3-4-5-6 
as directed in Article 10. Second, draw the axis X-Y, and 




FIG. 32. 



36 



ISOMETRIC DRAWING 



from the point o lay off a length o-o' equal to the height of the 
pyramid. Third, join each corner of the hexagon with the 
point o'. 
25. To Draw Any Rectangular Solid which is of Uniform or 

Similar Section. 

Fig. 33 is an illustration of a clamp block, and is, like the 
objects illustrated in Figs. 29 and 31, uniform in section, and 
is drawn in a similar manner. 

To construct the figure, first draw the center lines a-a and 
b-b. Second, working from the point o, lay off, each way, the 

lengths o-4, 4-3, etc., correspond- 
ing to the widths of the object 
as defined in drawing A . Third, 
working from point o, lay off 
the lengths o-r and o-s, as 
shown, corresponding to the 
thickness of the block . Fourth, 
through the points on each 
center line draw lines parallel 
to the other center line; the 
intersection of these two sets of 
lines will locate all points of the 
end face of the object, which 
may be drawn by joining the 
points as shown. Fifth, draw 
the axis X-Y and on it lay off, from point o, a length o-o' 
equal to the length of the block. Sixth, through the point o' 
draw the center lines c-c and d-d, and working to them draw 
the outline of the rear face of the block. Seventh, connect the 
two faces by joining the corners, and complete the figure, as 
shown. 

Attention is called to the similarity of the above construc- 
tion of the visible end face to that given for drawing any polygon, 
Article 12. It is as much " plotting " as the method there 
described. Also, note that the center lines used are not, exactly, 
what are usually termed center lines. The point to be noted is 
that the method or scheme for executing the construction of all 




FIG. 33. 



THE DRAWING OF SOLIDS 



37 



figures is similar, and that center lines may be used as base or 
reference lines. 

From Figs. 29, 31, and 33 it may be taken as a general 
construction for all objects which are uniform in section, to 
first construct the two ends or bases, then join the bases 
properly, forming the sides and completing the figure. 

Fig. 34 illustrates two objects which taper from one end to 
the other, objects of which a section at any point is similar to a 
section at any and all other points. Drawing A is a mechanical 
drawing of a crank blank, drawing B its isometric representation, 
and drawing C an isometric drawing of a steel key. 




FIG. 34. 

The method for constructing such figures is similar to that 
used when the section of the object drawn is uniform; that is, 
to first draw the two ends (end sections), then join the two as 
may be necessary to finish the figure. 

For example, to draw the steel key shown at (7, first draw 
the end section 1-2-3-4; second, the end section 5-6-7-8; 
and, third, join the sections as shown. 

The illustration of the crank is offered to show a very dif- 
ferent type of model from those given thus far, namely, objects 
of a rectangular nature; but it will be noted that the treatment 
or method of construction of the drawing is the same. To 
construct drawing B, first establish the three sets of center 
lines of the large end, as when drawing- the pyramid of blocks 



38 



ISOMETRIC DRAWING 



(Article 22), and working to them construct the three ellipses 
(Article 13) shown. Second, proceeding in a similar manner, 
construct the three ellipses of the small end of the figure. And, 
third, join up the two ends with tangent lines, as shown. 

26. To Draw Any Rectangular Solid of Variable Section. 

Fig. 35 is an illustration of a draughtsman's pencil-pointing 
pad, the handle of which varies in width. The construction 
of the drawing of this part of the object demonstrates a method 

of procedure applicable to the 
representation of any rect- 
angular object of variable 
section. 

The rectangular part of 
the figure (drawing B) is 
drawn in a manner similar to 
that illustrated in Fig. 30 and 
described in Article 22. To 
construct the drawing of the 
handle, first draw the center 
or base line, m-n. Second, 
divide this line into a num- 
ber of parts (such as by a 
FIG. 35. point every |" or |", or by 

taking points at places where 

the section of the object drawn changes) by marking off 
points such as points 1, 2, 3, etc. Third, through each 
point draw a line at right angles (so called in isometric 
drawing) to the line m-n (note that the line through any 
point is but a second center line), and on each line lay 
off, each way from the point on the line m-n, a length equal 
to one-half of the width of the handle at that point, obtain- 
ing the points a, 6, c, d, etc. Fourth, through the points 
thus located draw the curve, the outline of the handle, as 
shown. To draw the bottom curve, the line defining the 
thickness of the handle, draw vertical lines j-j' 9 i-4 r , etc., througn 
the points /, i, etc., and on each line Jay off a length equal to 




THE DRAWING OF SOLIDS 



39 



the thickness of the handle, locating points /', i' ', etc., and draw 
through these points as shown. 

The above example happens to be such that the curves 
drawn (on the top plane) are symmetrical with the center line 
m-n : should the case be different, a base line may be used for 
reference and from it the construction can be laid out, but the 
method is similar to that just described. 

27. To Draw a Cylinder. 

The drawing of a circle is given in Article 13, and the draw- 
ing of a solid of uniform section in Article 25, the drawing of a 
cylinder is based on these two constructions. 




5-2 



FIG. 36. 

Fig. 36 is an illustration of a right cylinder, drawing A being 
a mechanical drawing and drawings B-l and B-2 isometric 
drawings. 

To construct drawing B-l, first draw r the center lines a-b 
and c-d, and in accordance with Article 13 construct the ellipse 
of the upper base. Second, draw the axis of the cylinder, the 
line X-Yj and on it lay off the length o-o f equal to the length 
of the cylinder. Third, at the point o' establish the plane of 
the lower base by drawing the center lines af-b' and c'-d' and 
construct the ellipse a'-c'-b'-d' . Fourth, draw vertical lines 
tangent to the two bases, completing the figure. 

To construct drawing B-2, first draw the center lines a-b 
and c-d, and draw the ellipse representing the near end of the 



40 



ISOMETRIC DRAWING 




FIG. 37. 



cylinder in accordance with the above reference and as shown 
by the centers 1, 2, 3, and 4, and the radii R, S, r, and s. Second, 
shift the center points 1, 2, 3, and 4 along the lines 1-1', 2-2', 
etc. (parallel to the axisX-F), a distance equal to the length 

of the cylinder, and, with the 
new position of the center 
points, points 1', 2', 3', and 
4', as centers and the same 
radii as used to draw the 
front end of the cylinder; 
draw the rear end, as shown. 
Third, draw lines tangent to 
the two bases. 

28. To Draw a Cone. 

Fig. 37 illustrates the con- 
struction of a cone. 
To construct drawing B, first draw the center lines a-b and 
c-d, and working to them describe the ellipse a-c-b-d (Article 
13) of the base. Second, through the point o, draw the axis 
of the cone, the line X-Y, and on it lay off a length o-o' equal 
to the altitude or height of the cone. Third, from the point o' 
draw lines tangent to the base. 

29. To Draw a Solid Made 

Up of Circular Arcs and 

Straight Lines. 

Very often an object 
will have a number of 
curves which are circular 
arcs. When such is the 
case, the construction is 
similar to that described 
in Article 18. 

Fig. 38 illustrates the 
isometric drawing of two 
objects the lines of which are either straight lines or circular 
arcs. Drawing M represents a core box, and drawing N a cap 
for a bearing. 




FIG. 38. 



THE DRAWING OF SOLIDS 41 

To draw the circular arc showing at the bottom of the core 
box (arc a-d), consider the arc as extended to complete the 
circle of which it is a part; then lay out the construction for 
drawing a circle (Article 13), locate the center point and the 
radius for describing that portion of the ellipse covered by the 
arc in question (in this case, one-fourth of the circumference), 
and draw in the required curve. 

The drawing of the bearing cap is offered as a second example 
of the application of the above method of drawing parts of 
circles, and the construction, which is clearly shown in the 
figure, should be carefully noted. 

Attention is called to the arc at the bottom of the figure; 
this arc is drawn by dropping the point m to m' a length equal 
to the length of the object, and, with this new point as a center, 
and a radius s, the same radius used to draw the corresponding 
arc at the top, drawing it in, as shown. 

30. To Draw a Ring, Rectangular in Section. 

Fig. 39 illustrates the drawing of a ring which is rectangular 
in section. Drawing A is a mechanical drawing and drawings 
B-l, B-2, B-3, B-4, and B-5 are isometric drawings. The 
several isometric drawings are given to illustrate the choice 
of view or position of the object open to the draughtsmen. 

The figure should be compared with Fig. 9, and the similarity 
of position of the center lines and axis of the various drawings 
noted. For example, the position B-l corresponds to position 
d of Fig. 9, B-3 to 6, and position B-o to position c. The posi- 
tions B-2 and B-4 have no corresponding position shown in 
Fig. 9, but it will be noted that the relation of the lines used as 
center lines and axis is the same as in all isometric drawing, 
that is, adjacent lines forming an angle of 60, as shown. 

The construction of the several drawings is identical, and is 
illustrated in drawing B-l. To construct this drawing, first 
draw the center lines a-b and c-d, and working to them lay off, 
each way from the point o, a length equal to the radius of the 
inside of the ring, locating the points 1, 2, 3, and 4. Second, 
through these points draw the figure e-f-g-h, and within this 



42 



ISOMETRIC DRAWING 



the ellipse 1-2-3-4, all as directed for drawing the representa- 
tion of a circle in isometric, and as shown. Third, working 
to the same center lines, since the two circles of the end face 
are in the same plane, proceed in a similar manner and construct 
the ellipse 5-6-7-8. Fourth, draw such portions of the right 
end face of the ring as are visible, and finish the figure by draw- 
ing the two outside lines (top and bottom) tangent to the two 
bases. 

The lines of the drawing show every line of the construction. 
Attention is again called to the short method employed for 




FIG. 39. 

drawing the arcs of the ellipses showing in the rear base or end 
of the ring. For example, consider the outside curve at the 
rear, the line w'-S'-G'-/; this curve is parallel to the curve 
i/>-5-6-2 of the front face. To draw the arc at the rear, first 
draw through the points 5 and 6 the guide lines 5-5' and 6-6' 
parallel to the axis (line XY) of the ring. Second, draw a 
similar line through the point i, and on it lay off a length i-4 r 
equal to the thickness or length of the ring, and, with the point 
thus located, the point i', as a center and a radius H' equal to 
radius R, describe the arc 5'-6'. Third, in like manner shift 



THE DRAWING OF SOLIDS 



43 



the center point r to r', and s to s', and, with the new position 
of the points as centers and the same radius as used for the 
corresponding arc of the front face of the ring, describe the 
arcs o'-w' and G'-z', thus finishing the arc entire. 

31. To Draw a Circular Disc with Holes in it. 

Fig. 40 is an illustration of a disc with three equally spaced 
countersunk holes in it. 

To construct the figure, the disc may be considered as a short 
cylinder and its outline drawn accordingly (Article 27), the 





FIG. 40. 

center of the holes located by reference to the center lines of 
the top face of the disc, the planes of the circles representing 
the outline of the countersunk hole located as shown in Fig. 
30 and explained in Article 22, and the ellipse defining the holes 
drawn as explained in Article 13. 

The new feature introduced by this figure is the location 
and drawing of the countersunk holes. On the contrary, how- 
ever, the so-called " new feature " is not new, as the construc- 
tion is only the application of methods already known. The 
feature is an ever-recurrent one, and it is important that the 
student understand the method of procedure. 

Since it is correct practice to draw things square with the 
center lines when drawing objects such as the disc shown, 
square as many features with the center lines as possible. For 



44 



ISOMETRIC DRAWING 



example, if there should be but a single hole in the object, 
construct the drawing with the center of the hole on one of the 
center lines; if the object has two holes either 90 or 180 apart, 
see that they are located on the center lines; if the object has 
four holes equally spaced, place the centers on the center lines, 
etc. When there is an unequal number of holes, as in the present 
case of three, place one of the holes on one of the center lines, 
and, by plotting, referring the centers to the center lines, locate 
the centers for the other two holes as shown. 

It must always be borne in mind that an isometric drawing 
is not measured or laid out like a mechanical drawing, but 
that all dimensions must be laid out or taken in some one of 
three directions, that is, parallel to either center line or to the axis. 




FIG. 41, 

32. To Draw a Stepped Pulley. 

Fig. 41 is an illustration of a three-stepped cone pulley. 

To construct the figure (drawing B), first draw the center 
lines of the plane of the top face, the lines a-b and c-d, and 
working to them draw the outline of the hole through the center 
(Article 13; also see Fig. 42). Second, working to the same 
set of center lines, in similar manner draw the ellipse 5-6-7-8. 
Third, drop the three centers used to draw the arc z-6-5-2/ 



THE DRAWING OF SOLIDS 



45 



a distance equal to the dimension T and, with the same radii 
used to draw the above curve, draw the arc '-6'-5', all as 
directed for drawing the cylinder (Article 27) and as explained 
in connection with the construction of the drawing of the ring 
(Article 30). 

The remainder of the construction is similar to that already 
given, the procedure being to drop down the axis X-Y dis- 
tances T, S and E, locate the points o', o" and-o'", establish 
new planes at these points, and working to the center lines 
drawn draw in the several ellipses and complete the figure as 
shown. 

33. To Take Out a Section. 

In mechanical drawing it is customary when removing a 
section to remove some portion limited by the center lines. 
For example, in the case of the stepped pulley, Fig. 41, if a 
half section is to be shown, the quarter assumed to be removed 
would not be such a one as is 
included in the angle w-o-z 
(drawing A), but one such as 
is included in the angle c-a-b. 
This practice holds, also, in 
isometric drawing, and a sec- 
tion such as would show in 
the angle u-o-y of drawing 5, 
Fig. 41, is never given, the 
correct method being illustrated 
by Fig. 42. 

Fig. 42 illustrates the usual procedure for drawing an object 
with a section removed. The lines are all shown, and, in the 
light of what has been given thus far, the figure should prove 
self explanatory. 

When executing such as the above, two methods may be 
followed: (1) To first make the construction for the entire 
figure, then remove the section; (2) To make the construc- 
tion for only that portion of the object which is to show in the 
figure. The first construction is the safer for the beginner, 
and should be followed at first; after some experience the 




FIG. 42. 



46 



ISOMETRIC DRAWING 



work may be shortened in a number of ways which will then 
be apparent. 

34. To Draw an Eccentric. 

Fig. 43 is an illustration of a small eccentric blank. The 
dimensions are given on the mechanical drawing (.4) that the 
student may make the exact construction, should he care to do 
so. The figure does not introduce anything new, but is given 
as an example illustrating the inaccuracy of the method used 
for drawing the isometric representation of a circle. 




FIG. 43. 



The error of the method is discussed in paragraph (c) of 
Article 13, and is illustrated at the points M and N of drawing 
B, Fig. 43. If the method used were exact, the ellipse a-b-c-d 
and the ellipse 1-2-3^ would be tangent at the point M 
instead of intersecting; also, the slight discrepancy at point N 
would be eliminated. However, the drawing is but an illus- 
tration, and no harm is done when the curves are made to 
look right by joining them as shown. 

The student will, doubtless, encounter many similar con- 
ditions in his work. When such cases do occur, adjust the 



THE DRAWING OF SOLIDS 



47 



curves to match in such a way as to make the drawing appear 
natural. 

To construct drawing B, first consider the outer rim of the 
eccentric as a ring, and make the construction as directed in 
Article 30. Second, consider the hub, or center, as a cylinder, 
and make the construction as in Article 27. Third, locate 
the points o' by dimension, draw the ellipses 1-2-3-4 and 
5-6-7-8 as a guide, then adjust the curves to meet the ellipse 
a-b-c-d, as mentioned above. 

The^^ure shows such lines as will suggest the several steps 
necessa^r f or the construction, showing the particular radii 
and centers necessary to be shifted to draw the curves at the 
back, or rear, of the figure. 




FIG. 44. 

35. To Draw an Hexagonal Nut. 

In all machine drawing there are always a number of bolt 
heads and nuts to represent. Fig. 44 is given as illustrating a 
typical construction, the figure being the representation of an 
hexagonal nut. 

To construct the figure, first draw the center lines H-H and 
V-Vj and working to them construct the hexagon 1-2-3-4-5-6 
as directed in Article 10. Second, at each corner point of the 
hexagon erect a vertical line, and on each line lay off a length 
equal to the length of a corner of the nut, locating the points 
1', 2', 3', 4', 5', and 6'. Third, bisect each side of the hexagon 
1-2-3-4-5-6, at each middle point erect a vertical line, and on 
it lay off a length equal to the greatest width of a side of the nut, 



48 



ISOMETRIC DRAWING 



locating the points 7', 8', 9', 10', 11', and 12' and giving, with 
the two points already located, three points in the curve at the 
top of each side face of the nut. Fourth, draw a curved line 
(using the irregular curve) through the points thus located, as 
shown. Fifth, draw the axis X-Y through the point o, and on 
it lay off a length o-o' equal to the thickness of the nut. Sixth, 
through the point 0' draw the center lines a-b and c-d, and 
working to them draw the two circles showing in the top face 
of the nut, in accordance with Article 13, completing the figure. 




FIG. 45. 

36. To Draw a Hollow Cylinder with a Section Removed. 

Fig. 45 represents a hollow cylinder with a section removed 
and is offered to further illustrate the taking of sections in 
isometric drawing. 

To construct drawing B, proceed as directed in Article 27 
and as suggested by the lines of 'the figure, and draw the outline 
of the cylinder; then consider the hole through the cylinder 
as a second cylinder, and draw its outline in a similar manner. 
To take out the section, pass a plane e-f-g-h through the cylinder 
and on it draw the section of the cylinder, as shown; then remove 
the section between the plane of the front end and the section 
plane included between the planes l-l'-o'-o and 0-o'-2'-2, 
the construction being evident from the illustration. 



THE DRAWING OF SOLIDS 



49 



37. To Draw Any Solid of Revolution. 

Figs. 46 and 47 are illustrations of certain objects with no 
particular name, but typical of any object of revolution, that 




FIG. 46. 

is, any object a section at right angles to the axis of which is 
circle. 




FIG. 47. 



To draw such an object, pass a series of transverse sec- 
tional planes through it, draw the sections thus taken, then 



50 ISOMETRIC DRAWING 

draw the outline of the figure by drawing lines tangent to the 
sections. 

In the further discussion, sections used as above will be called 
" guide sections." 

To construct Fig. 46, first draw the axis X-Y and on it 
locate the points o, o' and o", according to dimensions as taken 
from drawing A or from the object. Second, at each of the 
three points draw center lines, and in accordance with Article 
13 (taking the diameters of the circles from drawing A) draw 




FIG. 48. 

the three ellipses, as shown. Third, draw tangent lines to the 
three ellipses, finishing the figure. 

The construction of Fig. 47 is similar to that of Fig. 46, 
the difference being that three intermediate guide planes are 
used instead of but one, and the outline of the figure is a curve 
instead of a straight line, as in Fig. 46. 

The use of guide sections is not limited to the construction 
of representations of solids of revolution, but may be used to 
advantage when drawing many other types of figures, as, for 
example, in Fig. 48, where the application is self evident. 



THE DRAWING OF SOLIDS 



51 



38. To Draw a Ring, Circular in Section. 

Fig. 49 illustrates a mechanical (A) and an isometric (B) 
drawing of a ring which is circular in section. 

To execute drawing B, first pass a number of radial planes 
through the ring, as indicated in drawing A, cutting the ring 
in a number of sections. Second, refer the center lines of each 
section of drawing A to the center lines of the figure (as indi- 
cated for section number 12), and by plotting establish their 
position in drawing B. Third, on each pair of center lines con- 
struct a parallelogram, and within each parallelogram describe 





FIG. 49. 

an ellipse. Fourth, draw lines tangent to the series of ellipses, 
all as suggested and shown by the figure. 

39. To Draw Screw Threads. 

To actually construct a correct representation of a screw 
thread is a somewhat difficult thing to do and consumes a con- 
siderable amount of time. In fact, such a procedure is so 
laborious and time-consuming that in ordinary mechanical 
drawing certain conventions are adopted to render the matter 
practical. This is also true of isometric drawing; for while 
it is possible to construct a true representation of a thread, it 
is not worth w r hile, as certain easily executed conventional 
methods of representation serve very w r ell. 

Fig. 50 illustrates one of the conventional representations 
mentioned, drawing A being a mechanical drawing and drawing 
B an isometric drawing. 



52 



ISOMETRIC DRAWING 



To construct the isometric drawing, first consider the object 
as a cylinder and construct the outline of the front and rear 
bases and connect them with tangent lines as directed in Article 
27. Second, on the plane of the front face of the cylinder 
draw the center lines H-H and V-V (these will be the same 
lines as used to obtain the ellipse of the front face), and working 
to them lay out the construction for the isometric representation 
of a circle of a diameter equal to the internal diameter of the 
thread (Article 13). Third, through the points b and e draw 



*1 








m 




- 









FIG. 50. 

the lines m-n and o-p, respectively. Fourth, beginning at the 
point numbered 1, lay off a series of divisions on the line X-Y 
equal to the distance between the top and bottom points of 
the thread ; then with the same radius as used to draw the arc 
b-e, and using each of the points 2, 3, 4, etc., as centers, draw 
a series of arcs parallel to arc b-e and terminated by the lines 
m-n and o-p. Fourth, through the center points used to draw 
the arcs b-c and d-e draw the lines r-s and t-u, respectively; 
lay off on each line a series of divisions equal to those laid off 
on the line X-Y, and, with the same radius as used to draw the 
arcs b-c and d-e, using each point as a center and picking up 



THE DRAWING OF SOLIDS 



53 



each of the arcs first drawn and terminated by the lines m-n 
and o-p, continue the curves until they disappear. 

Fig. 51 is an illustration of the object illustrated in Fig. 
50, showing a section removed and disclosing the points and roots 
of the thread. The outline of the figure and the arcs represent- 
ing the thread are draw r n as described for the construction of 
Fig. 50. The new feature introduced by the illustration is 
the construction of the section of the thread. 

The construction of the thread on either side is identical 
and is illustrated by the lines on the left side. To construct 
the thread, first draw the two 
guide lines on m-n and o-p a 
distance apart (measured along 
the center line b-c) equal to the 
depth of the thread. Second, lay 
off on line m-n a series of points 
1, 3, 5, 7, etc., a distance apart 
equal to the distance between 
points of the thread (equal to the 
pitch of the thread) . Third, bisect 
the length 1-3, and through the 
middle point draw the line r-s 
parallel to the center line b-c and cutting the line o-p in 2. 
Fourth, join the points 1 and 2; then through each point 
of division on the line m-n draw a line parallel to the line 
1-2 and terminating at the line o-p. Fifth, join the points 




FIG. 51. 




FIG. 52. 



2 and 3; then, proceeding as just described, draw the parallel 
lines 4-5, 6-7, etc., completing the construction. 



54 



ISOMETRIC DRAWING 




FIG. 53. 



Figs. 50 and 51 illustrate an inside thread. The construc- 
tion for an outside thread is similar, and is illustrated by Fig. 52. 
The parallel curves of Fig. 52 are, however, drawn at a distance 

apart equal to the pitch of the thread. 
The matter of the spacing of the 
center points and the resultant dis- 
tance between 'he curves is a matter 
of opinion with the draughtsman; it 
may be equal to the pitch, to one- 
half the pitch, or to something else. 
As a matter of fact, the whole 
scheme is but a representation 
to suggest the thread, and any 
combination that does this will 
answer. 

Square threads can be illustrated similarly to V-threads, 
as illustrated by Fig. 53. 

Fig. 54 illustrates three other conventions used to represent 
threads, the construction for each being similar to that already 
described. The short curve of 
No. 3 is drawn with a shorter 
radius than the middle por- 
tion of the longer curve, taken 
optionally by the draughts- 
man. 
40. To Draw a Sphere. 

To draw a sphere, execute 
the isometric representation of 

a circle of the same diameter as the sphere; then take as a radius 
a length equal to the semi-major axis of the ellipse so drawn, 
and draw a circle. The circle will be the isometric representa- 
tion of the sphere. 

The construction described above is illustrated in Fig. 55, 
drawing A 'being the mechanical drawing and drawing B the 
isometric drawing of the same sphere. 

Fig. 56 illustrates a good example of the application of the 
above construction. The figure illustrates a split-pattern of a 




No. 1. 



No. 2. 
FIG. 54. 



No. 3. 



THE DRAWING OF SOLIDS 



55 



small dumb-bell, drawing A being a mechanical drawing, 
drawing B-l an isometric drawing showing the pattern together, 




and drawing B-2 an isometric drawing showing the pattern 
separated. 




FIG. 56. 



Fig. 57 illustrates a good exercise for a beginner. The figures 
are all isometric drawings, drawing B representing a sphere 



56 ISOMETRIC DRAWING 

with a horizontal and two vertical (at right angles) great circles 




FIG. 57. 

on its surface. Drawing B-l illustrates the sphere cut in twc 

along the horizontal great circl( 
and the two halves separated 
Drawing B-2 illustrates th< 
sphere again cut in two (thi; 
time along one of the vertica 
great circles) and the parti 
separated, and drawing B-l 
shows it cut a third time anc 
the parts separated. 

Fig. 58, illustrating a hanc 
wheel, is also an excellent type 
of figure to draw to test one'* 
knowledge of the art and skil 
FIG. 58. in execution. 




CHAPTER IV 
A COURSE IN ISOMETRIC DRAWING 

41. Explanatory. 

The following exercises are offered as covering practically 
all of the different constructions given in Chapters II and III, 
and as comprising a brief course in isometric drawing. They 
may be followed exactly, or they may be used as examples 
only, and similar, original drawings made. It is suggested, 
however, that the course as outlined be followed out and then 
supplemented as the student or teacher may elect. 

The exercises are planned to go within a border line which 
is 8"X11" in dimensions, and a space 2"X3" is reserved for the 
title of the sheet. The sheets are all alike in this respect, Plate 
No. 4 showing the lay-out which is to be followed. 

57 



58 



ISOMETRIC DRAWING 




PLATE No. 4. 



A COURSE IN, ISOMETRIC DRAWING 59 



42. Sheet No. 1. 

Sheet No. 1 is an exercise in the drawing of some plane figures. 
The sheet is to be laid out, the figures located and drawn full 
size in accordance with the dimensions given, and the title 
filled in as shown. 

When inking-in, ink the border lines, the outlines of each 
figure, and its isometric center lines. Omit all dimensioning. 

The finished sheet is to have a margin \" wide all around 
outside the 8"Xll" border line, finishing 9"X12" in dimen- 
sions. 

The references for the several constructions are to be found 
in Chapter II. For drawings 1 and 2, see Article 9. For 
drawings 3 and 5, see Article 12. For drawing 4, see Article 

10. For drawings 6, 7, and 8, see Article 13. Drawing 9 is 
but the grouping of drawings 6, 7, and 8. For drawings 10 and 

11, see Article 13 (/). For drawings 12 and 16, see Article 13 
(d) and (e). For drawing 14, see Article 18. For drawing 17, 
see Article 17. 

To draw Fig. 13, locate the six points of a hexagon of 1J" 
diagonal diameter (Article 10) and the six points of a hexagon 
of }" diagonal diameter (the latter diagonal to be at right angles 
to the 1J" diagonal) and join the points as shown. 

To draw Fig. 15, locate the six points of a hexagon of 1" 
diagonal diameter (Article 10); through each of the six points 
thus located draw center lines and working to them (Article 
13) construct the isometric representation of a circle of \" 
diameter. 



60 



ISOMETRIC DRAWING 




PLATE No. 5. 



A COURSE IN- ISOMETRIC DRAWING 61 



43. Sheet No. 2. 

Sheet No. 2 is an exercise in the drawing of some straight- 
line objects. 

The dimensions for the sheet, directions for finishing, etc., 
are the same as for Sheet No. 1. 

The references for the several constructions are to be found 
in Chapter III. 

Drawing 1 represents two blocks piled one upon the other; 
drawing 2 represents a small two-drawer cabinet, showing the 
drawers pulled part way out; drawing 3 shows two rectangular 
frames pinned together at right angles one to the other; drawing 
5 is a representation of a minature stand; drawing 4, an illus- 
tration of the same stand stood upside down; drawing 6 shows 
a frustum of an hexagonal pyramid ; and drawing 7, an octagonal 
prism with a section removed. 

For drawings 1, 2, 3, 4, and 5, see Articles 21 and 22:, For 
drawing Fig. 6, see Article 24. The construction of the upper 
base of the frustum is left for the student to figure out, the 
upper base being at 30 with the lower base. For drawing 7, 
see Articles 24, 25, and 33. 



62 



ISOMETRIC DRAWING 




PLATE No. 6. 



A COURSE IN ISOMETRIC DRAWING 63 



44. Sheet No. 3. 

Sheet No. 3 is an exercise in the drawing of some ex- 
amples of bench work. 

The conditions for executing the sheet are the same as for 
Sheet No. 1. 

The sheet is very similar to Sheet No. 2, and is offered as 
giving additional practice in locating and drawing on different 
planes. 

Drawing 1 illustrates a half -splice; drawing 2, a pinned 
mortise-and-tenon joint, showing the pieces ready to assemble; 
drawing 4 is a keyed mortise-and-tenon joint, Fig. 3 being the 
key; drawing 5 shows a splayed splice; drawing 6 illustrates a 
plain dove-tailed joint; drawing 7, a blind dove-tailed joint; 
and drawing 8, a bench-hook. 

The reference for the entire sheet is to be found in Chapter 
III, the construction being based on Articles 21, 22, and 27. 



64 



ISOMETRIC DRAWING 




PLATE No. 7. 



A COURSE IN ISOMETRIC DRAWING 65 



45. Sheet No. 4. 

Sheet No. 4 is an exercise in the drawing of some cylindrical 
objects. 

The conditions for executing the sheet are the same as for 
Sheet No. 1. 

Drawing 1 is an illustration of a core-print; drawing 2 is a 
drawing of a circular nut; drawing 3 illustrates a core box; 
drawing 4 is a special, combination nut-and-spacer; and drawing 
5 a face-plate for a wood-turning lathe. 

The references for the several constructions are all to be 
found in Chapter III, and are: For Fig. 1, see Articles 27 and 37; 
for Fig. 2, see Articles 30 and 39; for Fig. 3, see Articles 21 and 
29; for Fig. 4, see Articles 27 and 35; for Fig. 5, see Articles 27, 
31 and 39. 



66 



ISOMETRIC DRAWING 




PLATE No. 8. 



A COURSE IN ISOMETRIC DRAWING 67 



46. Sheet No. 5. 

Sheet No. 5 is an exercise in the drawing of some shop tools. 

The sheet is offered as a suggestion only, and is not to be 
copied, no dimensions being given. 

To execute the sheet, it is suggested that the student obtain 
the same or similar tools as shown by the plate and, working 
from the tools, draw up an original sheet after the manner 
illustrated. 

The objects illustrated are (1) a cold chisel, (2) a claw hammer, 
(3) an alligator wrench, and (4) a plumb bob. 

All kinds of wrenches, hammers, mallets, screwdrivers, in 
short, the whole line of hand shop tools make very good examples 
to illustrate. 



68 ISOMETRIC DRAWING 

47. Suggested Sheets. 

The foregoing five sheets are given as typical exercises, and 
for further exercise work the student or teacher should have 
very little trouble in elaborating upon the course as given. 
To this end the following suggestions are offered : A sheet of 
shop tools other than those illustrated by Plate No. 8; a sheet 
of pipe fittings, such as tees, ells, union couplings, etc.; a sheet 
illustrating a globe or other type valve; a sheet illustrating a 
simple building, or some architectural construction or feature; 
or, in case the above suggestions are too advanced or the objects 
named not obtainable, books, blocks, desks, cabinets, and all 
kinds of furniture and household articles, such as spools, cups, 
glasses, stove parts, etc., may be used as examples. 

48. Remarks. 

Dimensioning. Isometric drawings are used more for illus- 
trating than for giving working directions working or shop 
drawings. Such being the case, they are not often dimensioned. 
As before expressed, however, they may be dimensioned, as 
witness Plates Nos. 4, 5, 6, and 7. 

The dimensions may be given in any way which will make 
them clear to the reader of the drawing, but they look best 
when applied to the drawing as on the above named plates. 

A reference to the plates will show that the dimensions 
apparently lie in the plane of the part dimensioned, and always 
in a direction parallel to one of the three isometric directions, 
that is, either parallel to one of the two center lines or to the 
axis of the drawing. This practice is recommended. 

Enlargement. An isometric drawing drawn full size will 
appear slightly larger than the object drawn. This feature 
will, doubtless, have been noted in looking over the figures 
of Chapter III, as, for example, Figs. 31, 44, 50, 55, and others. 
There is a reason for this, but it has no connection with the 
" How " of the art and is purposely not discussed further. 

Distortion. Some figures do not appear natural when illus- 
trated by an isometric drawing. This is particularly noticeable 
in objects of uniform section and of some length. The eye 
seems to instinctively sense that parallel lines should converge 



A COURSE IN ISOMETRIC DRAWIXG/A. : . . : : ' '-.8<K :' 

and, since, in isometric drawing they do not, the drawing 
appears distorted, as, for example, Figs. 50 and 52. This dis- 
tortion is so marked in some representations that it renders the 
art unsuited for illustrating that particular object. Distortion 
is one of the objections to isometric drawing. 

Shading. "While the examples given in the text are not 
shaded, or back-lined, it is not to be assumed that isometric 
drawings cannot be shaded. To shade an isometric drawing, 
make those lines heavy which represent the intersection of a 
light and a dark plane, or those lines which cut off the light 
the same as in ordinary mechanical drawing. 



ENGINEERING DRAWING 



BY 

THOMAS E. FRENCH 

Professor of Engineering Drawing, Ohio State University 



289 pages, 6x9, over 450 illustrations, $2.00 (8/6) net, postpaid 



CJ A general text on the language of 
drawing, with distinctive qualities in its 
breadth of scope, thoroughness, balance 
of treatment, and logical and topical 
arrangement. 

J The Author has had an unusual expe- 
rience both as a teacher and in practice. 
He was assisted by an especially compe- 
tent staff in the preparation of this book. 

<][ It covers modern practice in drawing 
in every branch of engineering, empha- 
sizing the practical value of the subject. 



MACHINE SHOP 
DRAWINGS 



BY 

FRED H. COLVIN 

Managing Editor, "American Machinist" 



180 pages, 4x7, illustrated, $1.00 (4/6) net, postpaid 



CJ A book intended to teacli the reading 
of drawings rather than drawing itself. 

fl It explains the representation of seen 
and unseen portions, the uses of lines, 
and of different views. It describes 
methods of laying out work and of 
simple sketching. 

t| The Author makes use of a broad 
practical experience in preparing a splen- 
did book for shop men. 

J It is a companion volume to 4 c Machine 
Shop Mechanics" and u Machine Shop 
Calculations. " It is a part of the Home 
Study Series. 



UNIVERSITY OF CALIFORNIA LIBRARY 
BERKELEY 

Return to desk from which borrowed. 
This book is DUE on the last date stamped below. 



DEC 3 1947 

l9)an'56TF 




!4Jan'57PWX 

iTVClv^ ~~ i^-sw 

JAN -14 1357 



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APR 1 



RECD 
DEC 8i1 



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-LD 21-100m-9,'47(A5702sl6)476